When are a prince's stats decided?

[Ironside]

If I said that I was referring to the way that they don't collect the marriage ring icon until after they have ascended to the throne, does that mean the two of us are talking about the same thing, or not?

Been a while since´playing but I recall that the classical inhierence where the royal brothers die rapidly together happens less with the muslims. Although the true test is to se if a new king messes up the hiers, as his children won't be showed until he's the new king.

What influences the amount of influence (no pun intended) a heir gets when he is coronated?

Is it the heirs stats? The amount of provinces under his control? The influence of the old king? all of the above?

I suspect all of the above (except possibly the amount of provinces by itself), but there's a clear link between very good stats on the hier and his starting influence. That's atleast 2 stats over 6 to get the royal line more self sustaining on giving good hiers.